Question
Find the reciprocal of the complex number z = 9 – 4i.
Solution
We are given the complex number: z = 9 – 4i We are to find its reciprocal , i.e., 1 / z To find the reciprocal of a complex number, multiply numerator and denominator by the conjugate of the denominator: 1 / (9 – 4i) × (9 + 4i) / (9 + 4i) = (9 + 4i) / [(9 – 4i)(9 + 4i)] = (9 + 4i) / (9² + 4²) = (9 + 4i) / (81 + 16) = (9 + 4i) / 97 So: 1 / z = 9/97 + 4i/97
A man standing on the top of a cliff observes a boat at an angle of depression of 45°. He then moves 30 meters further down the cliff, and the angle of...
A square prism has a base side of 10 cm and a height of 15 cm. If a cone with the same base and height is removed from the prism, what is the volume of ...
What type of high-performance and costly computer can process data for hundreds or thousands of users at the same time?
A car travels a distance of 240 km in 4 hours. If it increases its speed by 20 km/h for the next 3 hours, how much distance will it cover in total?
What will be come in place of (?) in the given number series.
1, 8, 27, ?, 125, 216120 124 151 167 292 ?
A, B, and C together can do a work alone in 12 days, 18 days, and 54 days respectively. A alone starts the work and work for 3 days and leaves the work,...
Find the area enclosed between the curves y=(x−4)2 and y=16−x2over their intersection interval.
A vessel contains 80 liters of milk. 16 liters of milk are taken out and replaced with water. This process is repeated once more time. Find the quantity...
I. 3x2 – 15x + 18 = 0
II. 2y2 – 40y + 198 = 0
Relevant for Exams:
